As far as what appears to be a thawing of the bitter partisanship in Washington with last week's bipartisan budget deal, the AIG chief said he's not very optimistic.

"It's great when you take a couple of very competent Congress people and put them in a room and get this worked out," he said. "But that doesn't mean the rest of government has the right leadership to get the [country] optimistic and on the right track."

Case in point, Senate Democrats are still short of the votes needed to pass a budget deal that would avoid a government shutdown in January and blunt automatic spending cuts. "We will need about eight Republicans to come our way," Sen. Dick Durbin—the No. 2 Democrat in the chamber—told CBS "Face the Nation" Sunday.

One year anniversary for AIG

Saturday marked the first anniversary of the full resolution of the government's financial support of AIG with the completion of an offering of approximately 234.2 million shares of the insurer's common stock by the Treasury Department.

All told, Treasury said it made nearly $23 billion on its investment.

Benmosche, a former MetLife CEO, came out of retirement in 2009—tasked with bringing AIG back from the dead, after the $182 billion taxpayer buyout of the insurance giant that year before.

AIG has since been designated as a systemically important financial institution, known by the acronym SIFI.

"SIFI is not a bad thing. Run your company the right way and chances are you'll be fine," Benmosche said. "Like it or not, when you're big and you make promises and guarantees with people's lifetimes you have to have somebody overseeing that."

He said the money market industry should be considered systemically important. "That's a run where you could see several trillion dollars coming out of the market and going right into a banking institution for safety," Benmosche said, "and that I worry about more than people who invest in stocks and bonds who understand there's a risk."

Obamacare concerns

As for Obamacare, Benmosche thinks one of the cornerstones of the new health-care law is flawed. "Having more access and thinking that healthy people are going to come into the system to pay for the unhealthy, I think is a failed strategy."

AIG doesn't offer health insurance, but as an observer of the industry, he added, "What's more important is to think about things like tort reform to begin to make sure doctors aren't afraid to practice."

CORRECTION: This version corrected that Saturday was the first anniversary of the resolution of the government's financial support for AIG.